The Complete Guide to Option Pricing Formulas

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ISBN: 9780071389976 | 0071389970
Cover: Hardcover
Copyright: 1/8/2007

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Since it was first published in 1997, The Complete Guide to Option Pricing Formulas has become the "bible" in the world of options, providing traders and investors with virtually every option formula. Now completely updated and extensively expanded, the Second Edition of this classic financial resource is more than twice as long as the First Edition, covering a wide range of new and different types of options as well as the pricing models for them.

Introduction	p. xvii
Acknowledgments	p. xix
What Is New in the Second Edition?	p. xxi
Option Pricing Formulas Overview	p. xxiii
Glossary of Notations	p. xxxv
Black-Scholes-Merton	p. 1
Black-Scholes-Merton	p. 2
The Black-Scholes Option Pricing Formula	p. 2
Options on Stock Indexes	p. 4
Options on Futures	p. 4
Margined Options on Futures	p. 5
Currency Options	p. 6
The Generalized Black-Scholes-Merton Option Pricing Formula	p. 7
Parities and Symmetries	p. 9
Put-Call Parity for European Options	p. 9
At-the-Money Forward Value Symmetry	p. 10
Put-Call Symmetry	p. 10
Put-Call Supersymmetry	p. 11
Black-Scholes-Merton on Variance Form	p. 11
Before Black-Scholes-Merton	p. 12
The Bachelier Model	p. 12
The Sprenkle Model	p. 13
The Boness Model	p. 14
The Samuelson Model	p. 14
Appendix A: The Black-Scholes-Merton PDE	p. 15
Ito's Lemma	p. 15
Dynamic Hedging	p. 16
Black-Scholes-Merton Greeks	p. 21
Delta Greeks	p. 21
Delta	p. 21
Delta Mirror Strikes and Assets	p. 29
Strike from Delta	p. 30
Futures Delta from Spot Delta	p. 31
DdeltaDvol and DvegaDspot	p. 32
DvannaDvol	p. 34
DdeltaDtime, Charm	p. 35
Elasticity	p. 36
Gamma Greeks	p. 38
Gamma	p. 38
Maximal Gamma and the Illusions of Risk	p. 39
GammaP	p. 42
Gamma Symmetry	p. 45
DgammaDvol, Zomma	p. 45
DgammaDspot, Speed	p. 47
DgammaDtime, Color	p. 49
Vega Greeks	p. 50
Vega	p. 50
Vega Symmetry	p. 55
Vega-Gamma Relationship	p. 55
Vega from Delta	p. 56
VegaP	p. 56
Vega Leverage, Vega Elasticity	p. 57
DvegaDvol, Vomma	p. 57
DvommaDvol, Ultima	p. 60
DvegaDtime	p. 61
Variance Greeks	p. 62
Variance Vega	p. 62
DdeltaDvar	p. 63
Variance Vomma	p. 63
Variance Ultima	p. 63
Volatility-Time Greeks	p. 64
Theta Greeks	p. 64
Theta	p. 64
Theta Symmetry	p. 68
Rho Greeks	p. 68
Rho	p. 68
Phi/Rho-2	p. 71
Carry Rho	p. 73
Probability Greeks	p. 75
In-the-Money Probability	p. 76
DzetaDvol	p. 79
DzetaDtime	p. 80
Risk-Neutral Probability Density	p. 80
From in-the-Money Probability to Density	p. 80
Probability of Ever Getting in-the-Money	p. 80
Greeks Aggregations	p. 81
Net Weighted Vega Exposure	p. 82
At-the-Money Forward Approximations	p. 84
Approximation of the Black-Scholes-Merton Formula	p. 84
Delta	p. 84
Gamma	p. 84
Vega	p. 84
Theta	p. 84
Rho	p. 85
Cost-of-Carry	p. 85
Numerical Greeks	p. 85
First-Order Greeks	p. 85
Second-Order Greeks	p. 86
Third-Order Greeks	p. 86
Mixed Greeks	p. 87
Third-Order Mixed Greeks	p. 87
Greeks from Closed-Form Approximations	p. 89
Appendix B: Taking Partial Derivatives	p. 90
Analytical Formulas for American Options	p. 97
The Barone-Adesi and Whaley Approximation	p. 97
The Bjerksund and Stensland (1993) Approximation	p. 101
The Bjerksund and Stensland (2002) Approximation	p. 104
Put-Call Transformation American Options	p. 109
American Perpetual Options	p. 109
Exotic Options-Single Asset	p. 111
Variable Purchase Options	p. 111
Executive Stock Options	p. 114
Moneyness Options	p. 114
Power Contracts and Power Options	p. 115
Power Contracts	p. 115
Standard Power Option	p. 116
Capped Power Option	p. 117
Powered Option	p. 118
Log Contracts	p. 119
Log(S) Contract	p. 120
Log Option	p. 121
Forward Start Options	p. 121
Fade-in Option	p. 122
Ratchet Options	p. 124
Reset Strike Options-Type 1	p. 124
Reset Strike Options-Type 2	p. 125
Time-Switch Options	p. 127
Chooser Options	p. 128
Simple Chooser Options	p. 128
Complex Chooser Options	p. 129
Options on Options	p. 132
Put-Call Parity Compound Options	p. 135
Compound Option Approximation	p. 136
Options with Extendible Maturities	p. 138
Options That Can Be Extended by the Holder	p. 138
Writer-Extendible Options	p. 140
Lookback Options	p. 141
Floating-Strike Lookback Options	p. 141
Fixed-Strike Lookback Options	p. 143
Partial-Time Floating-Strike Lookback Options	p. 144
Partial-Time Fixed-Strike Lookback Options	p. 147
Extreme-Spread Options	p. 148
Mirror Options	p. 150
Barrier Options	p. 152
Standard Barrier Options	p. 152
Standard American Barrier Options	p. 154
Double-Barrier Options	p. 156
Partial-Time Single-Asset Barrier Options	p. 160
Look-Barrier Options	p. 163
Discrete-Barrier Options	p. 164
Soft-Barrier Options	p. 165
Use of Put-Call Symmetry for Barrier Options	p. 167
Barrier Option Symmetries	p. 168
First-Then-Barrier Options	p. 169
Double-Barrier Option Using Barrier Symmetry	p. 171
Dual Double-Barrier Options	p. 172
Binary Options	p. 174
Gap Options	p. 174
Cash-or-Nothing Options	p. 174
Asset-or-Nothing Options	p. 175
Supershare Options	p. 176
Binary Barrier Options	p. 176
Double-Barrier Binary Options	p. 180
Double-Barrier Binary Asymmetrical	p. 181
Asian Options	p. 182
Geometric Average-Rate Options	p. 182
Arithmetic Average-Rate Options	p. 186
Discrete Arithmetic Average-Rate Options	p. 192
Equivalence of Floating-Strike and Fixed-Strike Asian Options	p. 199
Asian Options with Volatility Term-Structure	p. 199
Exotic Options on Two Assets	p. 203
Relative Outperformance Options	p. 203
Product Options	p. 205
Two-Asset Correlation Options	p. 205
Exchange-One-Asset-for-Another Options	p. 206
American Exchange-One-Asset-for-Another Option	p. 208
Exchange Options on Exchange Options	p. 209
Options on the Maximum or the Minimum of Two Risky Assets	p. 211
Spread-Option Approximation	p. 213
Two-Asset Barrier Options	p. 215
Partial-Time Two-Asset Barrier Options	p. 217
Margrabe Barrier Options	p. 219
Discrete-Barrier Options	p. 221
Two-Asset Cash-or-Nothing Options	p. 221
Best or Worst Cash-or-Nothing Options	p. 223
Options on the Minimum or Maximum of Two Averages	p. 224
Currency-Translated Options	p. 226
Foreign Equity Options Struck in Domestic Currency	p. 226
Fixed Exchange Rate Foreign Equity Options	p. 228
Equity Linked Foreign Exchange Options	p. 230
Takeover Foreign Exchange Options	p. 232
Greeks for Two-Asset Options	p. 232
Black-Scholes-Merton Adjustments and Alternatives	p. 233
The Black-Scholes-Merton Model with Delayed Settlement	p. 234
The Black-Scholes-Merton Model Adjusted for Trading Day Volatility	p. 235
Discrete Hedging	p. 236
Hedging Error	p. 236
Discrete-Time Option Valuation and Delta Hedging	p. 237
Discrete-Time Hedging with Transaction Cost	p. 238
Option Pricing in Trending Markets	p. 240
Alternative Stochastic Processes	p. 242
Constant Elasticity of Variance	p. 242
Skewness-Kurtosis Models	p. 244
Definition of Skewness and Kurtosis	p. 244
The Skewness and Kurtosis for a Lognormal Distribution	p. 245
Jarrow and Rudd Skewness and Kurtosis Model	p. 246
The Corrado and Su Skewness and Kurtosis Model	p. 247
Modified Corrado-Su Skewness-Kurtosis Model	p. 250
Skewness-Kurtosis Put-Call Supersymmetry	p. 252
Skewness-Kurtosis Equivalent Black-Scholes-Merton Volatility	p. 252
Gram Charlier Density	p. 252
Skewness-Kurtosis Trees	p. 253
Pascal Distribution and Option Pricing	p. 253
Jump-Diffusion Models	p. 253
The Merton Jump-Diffusion Model	p. 253
Bates Generalized Jump-Diffusion Model	p. 255
Stochastic Volatility Models	p. 258
Hull-White Uncorrelated Stochastic Volatility Model	p. 259
Hull-White Correlated Stochastic Volatility Model	p. 261
The SABR Model	p. 265
Variance and Volatility Swaps	p. 271
Variance Swaps	p. 271
Volatility Swaps	p. 274
More Information	p. 278
Trees and Finite Difference Methods	p. 279
Binomial Option Pricing	p. 279
Cox-Ross-Rubinstein American Binomial Tree	p. 284
Greeks in CRR Binomial Tree	p. 287
Rendleman Bartter Binomial Tree	p. 289
Leisen-Reimer Binomial Tree	p. 290
Convertible Bonds in Binomial Trees	p. 292
Binomial Model with Skewness and Kurtosis	p. 297
Trinomial Trees	p. 299
Exotic Options in Tree Models	p. 303
Options on Options	p. 303
Barrier Options Using Brownian Bridge Probabilities	p. 305
American Barrier Options in CRR Binomial Tree	p. 307
European Reset Options Binomial	p. 308
American Asian Options in a Tree	p. 314
Three-Dimensional Binomial Trees	p. 315
Implied Tree Models	p. 321
Implied Binomial Trees	p. 321
Implied Trinomial Trees	p. 327
Finite Difference Methods	p. 334
Explicit Finite Difference	p. 335
Implicit Finite Difference	p. 338
Finite Difference in ln(S)	p. 340
The Crank-Nicolson Method	p. 342
Monte Carlo Simulation	p. 345
Standard Monte Carlo Simulation	p. 345
Greeks in Monte Carlo	p. 347
Monte Carlo for Callable Options	p. 349
Two Assets	p. 350
Three Assets	p. 352
N Assets, Cholesky Decomposition	p. 353
Monte Carlo of Mean Reversion	p. 355
Generating Pseudo-Random Numbers	p. 356
Variance Reduction Techniques	p. 358
Antithetic Variance Reduction	p. 358
IQ-MC/Importance Sampling	p. 359
IQ-MC Two Correlated Assets	p. 361
Quasi-Random Monte Carlo	p. 362
American Option Monte Carlo	p. 364
Options on Stocks That Pay Discrete Dividends	p. 367
European Options on Stock with Discrete Cash Dividend	p. 368
The Escrowed Dividend Model	p. 368
Simple Volatility Adjustment	p. 369
Haug-Haug Volatility Adjustment	p. 369
Bos-Gairat-Shepeleva Volatility Adjustment	p. 370
Bos-Vandermark	p. 371
Non-Recombining Tree	p. 372
Black's Method for Calls on Stocks with Known Dividends	p. 375
The Roll, Geske, and Whaley Model	p. 375
Benchmark Model for Discrete Cash Dividend	p. 378
A Single Dividend	p. 378
Multiple Dividends	p. 382
Applications	p. 382
Options on Stocks with Discrete Dividend Yield	p. 390
European with Discrete Dividend Yield	p. 390
Closed-Form American Call	p. 390
Recombining Tree Model	p. 393
Commodity and Energy Options	p. 397
Energy Swaps/Forwards	p. 397
Energy Options	p. 400
Options on Forwards, Black-76F	p. 400
Energy Swaptions	p. 401
Hybrid Payoff Energy Swaptions	p. 405
The Miltersen-Schwartz Model	p. 406
Mean Reversion Model	p. 410
Seasonality	p. 411
Interest Rate Derivatives	p. 413
FRAs and Money Market Instruments	p. 413
FRAs From Cash Deposits	p. 413
The Relationship between FRAs and Currency Forwards	p. 414
Convexity Adjustment Money Market Futures	p. 415
Simple Bond Mathematics	p. 417
Dirty and Clean Bond Price	p. 417
Current Yield	p. 417
Modified Duration and BPV	p. 417
Bond Price and Yield Relationship	p. 418
Price and Yield Relationship for a Bond	p. 418
From Bond Price to Yield	p. 419
Pricing Interest Rate Options Using Black-76	p. 419
Options on Money Market Futures	p. 420
Price and Yield Volatility in Money Market Futures	p. 421
Caps and Floors	p. 421
Swaptions	p. 422
Swaption Volatilities from Caps or FRA Volatilities	p. 424
Swaptions with Stochastic Volatility	p. 425
Convexity Adjustments	p. 425
European Short-Term Bond Options	p. 427
From Price to Yield Volatility in Bonds	p. 428
The Schaefer and Schwartz Model	p. 428
One-Factor Term Structure Models	p. 429
The Rendleman and Bartter Model	p. 429
The Vasicek Model	p. 430
The Ho and Lee Model	p. 432
The Hull and White Model	p. 433
The Black-Derman-Toy Model	p. 434
Volatility and Correlation	p. 445
Historical Volatility	p. 445
Historical Volatility from Close Prices	p. 445
High-Low Volatility	p. 447
High-Low-Close Volatility	p. 448
Exponential Weighted Historical Volatility	p. 449
From Annual Volatility to Daily Volatility	p. 450
Confidence Intervals for the Volatility Estimate	p. 451
Volatility Cones	p. 452
Implied Volatility	p. 453
The Newton-Raphson Method	p. 453
The Bisection Method	p. 455
Implied Volatility Approximations	p. 456
Implied Forward Volatility	p. 458
From Implied Volatility Surface to Local Volatility Surface	p. 458
Confidence Interval for the Asset Price	p. 459
Basket Volatility	p. 460
Historical Correlation	p. 460
Distribution of Historical Correlation Coefficient	p. 461
Implied Correlations	p. 462
Implied Correlation from Currency Options	p. 462
Average Implied Index Correlation	p. 462
Various Formulas	p. 463
Probability of High or Low, the Arctangent Rule	p. 463
Siegel's Paradox and Volatility Ratio Effect	p. 464
Distributions	p. 465
The Cumulative Normal Distribution Function	p. 465
The Hart Algorithm	p. 465
Polynomial Approximations	p. 467
The Inverse Cumulative Normal Distribution Function	p. 469
The Bivariate Normal Density Function	p. 470
The Cumulative Bivariate Normal Distribution Function	p. 470
The Trivariate Cumulative Normal Distribution Function	p. 482
Some Useful Formulas	p. 487
Interpolation	p. 487
Linear Interpolation	p. 487
Log-Linear Interpolation	p. 487
Exponential Interpolation	p. 487
Cubic Interpolation: Lagrange's Formula	p. 488
Cubic-Spline Interpolation	p. 488
Two-Dimensional Interpolation	p. 490
Interest Rates	p. 491
Future Value of Annuity	p. 491
Net Present Value of Annuity	p. 491
Continuous Compounding	p. 491
Compounding Frequency	p. 491
Zero-Coupon Rates from Par Bonds/Par Swaps	p. 492
Risk-Reward Measures	p. 493
Treynor's Measure	p. 493
Sharpe Ratio	p. 494
Confidence Ratio	p. 494
Sortino Ratio	p. 495
Burke Ratio	p. 495
Return on VaR	p. 495
Jensen's Measure	p. 496
Appendix C: Basic Useful Information	p. 496
The Option Pricing Software	p. 497
Bibliography	p. 499
Index	p. 521
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The Complete Guide to Option Pricing Formulas

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